## A Comparison of Two Approaches to Splitting Default Theories (1997)

Venue: | In AAAI/IAAI |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Antoniou97acomparison,

author = {Grigoris Antoniou},

title = {A Comparison of Two Approaches to Splitting Default Theories},

booktitle = {In AAAI/IAAI},

year = {1997},

pages = {424--429}

}

### OpenURL

### Abstract

Default logic is computationally expensive. One of the most promising ways of easing this problem and developing powerful implementations is to split a default theory into smaller parts and compute extensions in a modular, "local" way. This paper compares two recent approaches, Turner's splitting and Cholewinski's stratification. It shows that the approaches are closely related -- in fact the former can be viewed as a special case of the latter. 1 Introduction Default logic (Reiter 1980) is one of the most prominent approaches of nonmonotonic reasoning, since it provides a formal theory of reasoning based on default rules. One of the main problems with its applicability is that it is computationally harder than classical logic (Marek and Truszczynski 1993, Gottlob 1992), which makes the implementation of powerful systems difficult. A possible solution to this problem might be to split the available knowledge into smaller parts, and to apply default reasoning in a local way. This idea...

### Citations

1423 |
A Logic for Default Reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...urner's splitting and Cholewinski's stratification. It shows that the approaches are closely related -- in fact the former can be viewed as a special case of the latter. 1 Introduction Default logic (=-=Reiter 1980-=-) is one of the most prominent approaches of nonmonotonic reasoning, since it provides a formal theory of reasoning based on default rules. One of the main problems with its applicability is that it i... |

260 | Splitting a logic program
- Lifschitz, Turner
- 1994
(Show Context)
Citation Context ...ped at the University of Kentucky (Cholewinski et al. 1995). (Turner 1996) presented an alternative approach of splitting a default theory. It is an adaption of a similar idea from logic programming (=-=Lifschitz and Turner 1994-=-), and makes use of a sort of partial evaluation. In this paper we compare these two approaches. Reasons why such a comparison is useful include the following: (i) It can lead to a better understandin... |

242 | Logic programming and negation: a survey
- Apt, Bol
- 1994
(Show Context)
Citation Context ...es of papers (Cholewinski 1994, 1995a, 1995b) Cholewinski introduced and studied stratification of default theories. His idea was to take up the notion of stratification known from logic programming (=-=Apt and Bol 1994-=-) and expand it to suit the necessities of default logic (it needs to treat negation, too). Essentially, his approach is based on the 1 Copyright c fl1997, American Association for Artificial Intellig... |

178 |
Complexity results for nonmonotonic logics
- Gottlob
- 1992
(Show Context)
Citation Context ...t provides a formal theory of reasoning based on default rules. One of the main problems with its applicability is that it is computationally harder than classical logic (Marek and Truszczynski 1993, =-=Gottlob 1992-=-), which makes the implementation of powerful systems difficult. A possible solution to this problem might be to split the available knowledge into smaller parts, and to apply default reasoning in a l... |

115 |
Nonmonotonic Reasoning
- Antoniou
- 1997
(Show Context)
Citation Context ...d. Note that in case \Pi is successful, every justification / of a default in \Pi is consistent with In(\Pi). ffl \Pi is closed iff every default that is applicable to In(\Pi) already occurs in \Pi. (=-=Antoniou 1997-=-) shows that Reiter's original definition of extensions is equivalent to the following one: A set of formulae E is an extension of a default theory T iff there is a closed and successful process \Pi o... |

64 |
Nonmonotonic Logics
- Marek, Truszczyński
- 1993
(Show Context)
Citation Context ...nmonotonic reasoning, since it provides a formal theory of reasoning based on default rules. One of the main problems with its applicability is that it is computationally harder than classical logic (=-=Marek and Truszczynski 1993-=-, Gottlob 1992), which makes the implementation of powerful systems difficult. A possible solution to this problem might be to split the available knowledge into smaller parts, and to apply default re... |

39 | Computing with default logic
- Cholewiński, Marek, et al.
- 1999
(Show Context)
Citation Context ...applysffi before ffi 0 . This way we obtain information about potential orderings of defaults. Based on this idea, a powerful system for default reasoning was developed at the University of Kentucky (=-=Cholewinski et al. 1995-=-). (Turner 1996) presented an alternative approach of splitting a default theory. It is an adaption of a similar idea from logic programming (Lifschitz and Turner 1994), and makes use of a sort of par... |

38 | Alternative approaches to default logic - Delgrande, Schaub, et al. - 1994 |

17 | Reasoning with stratified default theories
- Cholewiński
- 1995
(Show Context)
Citation Context ...ed separately. In fact there is no reason why ffi 2 should be applied before ffi 3 , or the other way around. Cholewinski pushed this observation further by studying partial orderings between strata (=-=Cholewinski 1995-=-a), leading to a much more efficient implementation. 3 Prop(ffi 0 ) is the set of all propositional atoms occurring in ffi 0 . Splitting default theories Following Turner's presentation, we consider a... |

16 | Constrained and rational default logics
- Mikitiuk, Truszczynski
- 1995
(Show Context)
Citation Context ...eral variants that have been proposed in the literature, such as Justified Default Logic (Lukaszewicz 1988), Constrained Default Logic (Delgrande, Schaub and Jackson 1994) and Rational Default Logic (=-=Mikitiuk and Truszczynski 1995). The ide-=-a of stratification can be adapted to these logics in a straightforward way. What varies from logic to logic is what it means for a default to "make use" of information provided by another. ... |

15 | Stratified default theories
- Cholewiński
(Show Context)
Citation Context ...ed separately. In fact there is no reason why ffi 2 should be applied before ffi 3 , or the other way around. Cholewinski pushed this observation further by studying partial orderings between strata (=-=Cholewinski 1995-=-a), leading to a much more efficient implementation. 3 Prop(ffi 0 ) is the set of all propositional atoms occurring in ffi 0 . Splitting default theories Following Turner's presentation, we consider a... |

10 |
Stratified default logic
- Cholewinski
- 1994
(Show Context)
Citation Context ...l default logic applied to the entire knowledge base. In contrast to this, two other approaches were introduced which split a default theory in a way that preserves extensions. In a series of papers (=-=Cholewinski 1994-=-, 1995a, 1995b) Cholewinski introduced and studied stratification of default theories. His idea was to take up the notion of stratification known from logic programming (Apt and Bol 1994) and expand i... |

8 | Toward efficient default reasoning
- Etherington, Crawford
- 1996
(Show Context)
Citation Context ...to smaller parts, and to apply default reasoning in a local way. This idea has been around for quite a while, but it is only quite recently that formal approaches were proposed to achieve this goal. (=-=Etherington and Crawford 1996) propose -=-restriction of the search space to a "relevant portion" of the knowledge base; their approach will usually deliver different results than the classical default logic applied to the entire kn... |